Bergmans and Cover identified the capacity region of the Gaussian degraded broadcast channel, where different receivers observe the transmitted signal to noise ratios. This paper presents a superposition turbo coding scheme that performs within 1 dB of the capacity region boundary of the degraded broadcast channel at BER of 10-5. Performance is consistent over the entire useful range of the power allocation parameter α. Coding for the degraded broadcast channel is equivalent to coding for unequal error protection. Adjusting α changes the transmitter constellation of our encoder, and changes the degree to which error protection is unequal. When α is selected to provide equal error protection, the code is essentially a multilevel turbo trellis-coded-modulation schemes with the advantage of the potential for flexible unequal error protection as α is varied.